I run exactly the same setup you have but on a little wider rim, 17x8.
This is a great setup for the track you have for sale. I would jump on at least the tires but I run 245/40/17 because I have full aero and narrower does not last me much. In any case, my friend Rick just picked up a used FRS and I sent him a text with the information on this thread. This would be perfect for him. Good luck with the sale.